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Area of Science:

  • Quantum mechanics
  • Statistical physics

Background:

  • Energy eigenstates in quantum systems possess distinct properties.
  • Classifiers can categorize these eigenstates based on their features.

Purpose of the Study:

  • To investigate the invariance of energy eigenstate ratios within energy shells.
  • To establish the general applicability of this self-similarity in quantum systems.

Main Methods:

  • Analysis of energy shells with width ΔE and Planck constant ℏ.
  • Numerical simulations on diverse quantum systems (circular billiard, double top model, kicked rotor, Heisenberg XXZ model).

Main Results:

  • The ratio of eigenstate types within an energy shell is invariant under changes in ΔE and ℏ.
  • This invariance holds when the number of eigenstates is statistically significant.

Conclusions:

  • Self-similarity in energy eigenstates is a general characteristic of quantum systems.
  • Numerical evidence supports the theoretical argument for this general feature.